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Home » Check: Is 14 $ \equiv 1 \pmod13 $? - 500apps

Check: Is 14 $ \equiv 1 \pmod13 $? - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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\left| rac{3 - 2y}{y - 2}
ight| \leq 1 \Rightarrow (3 - 2y)^2 \leq (y - 2)^2
Expand both sides:
- 12y + 4y^2 \leq y^2 - 4y + 4
4y^2 - 12y + 9 \leq y^2 - 4y + 4
3y^2 - 8y + 5 \leq 0
Solve quadratic: discriminant = \(64 - 60 = 4\), roots:
y = rac{8 \pm 2}{6} = rac{10}{6} = rac{5}{3},\quad rac{6}{6} = 1
So \(1 \leq y \leq rac{5}{3}\)
Check if all values are attainable: at \(\sin x = 1\), \(f = rac{2+3}...

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